Nonnegative matrix decomposition

Given partial observations of a nonnegative matrix (let Omega index the observed entries), the problem seeks nonnegative matrices and such that $mathcal{P}_Omega(XY) =mathcal{P}_Omega(M)$ or $mathcal{P}_Omega(XY)approx mathcal{P}_Omega(M)$ .

The model is

$mathop{mathrm{minimize}}_{Xge 0,Yge 0} ~frac{1}{2}|mathcal{P}_Omega(XY - M)|_F^2.$

The algorithm is described in Algorithm 2 of this report.

Matlab code of BCU with prox-linear update and extrapolation

Matlab function
Synthetic example